<?php
    require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/trend/bestFitClass.php';
    require_once PHPEXCEL_ROOT . 'PHPExcel/Shared/JAMA/Matrix.php';

    /**
     * PHPExcel_Polynomial_Best_Fit
     * Copyright (c) 2006 - 2015 PHPExcel
     * This library is free software; you can redistribute it and/or
     * modify it under the terms of the GNU Lesser General Public
     * License as published by the Free Software Foundation; either
     * version 2.1 of the License, or (at your option) any later version.
     * This library is distributed in the hope that it will be useful,
     * but WITHOUT ANY WARRANTY; without even the implied warranty of
     * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
     * Lesser General Public License for more details.
     * You should have received a copy of the GNU Lesser General Public
     * License along with this library; if not, write to the Free Software
     * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
     * @category   PHPExcel
     * @package    PHPExcel_Shared_Trend
     * @copyright  Copyright (c) 2006 - 2015 PHPExcel (http://www.codeplex.com/PHPExcel)
     * @license    http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
     * @version    ##VERSION##, ##DATE##
     */
    class PHPExcel_Polynomial_Best_Fit extends PHPExcel_Best_Fit {
        /**
         * Algorithm type to use for best-fit
         * (Name of this trend class)
         * @var    string
         **/
        protected $bestFitType = 'polynomial';
        /**
         * Polynomial order
         * @protected
         * @var    int
         **/
        protected $order = 0;

        /**
         * Define the regression and calculate the goodness of fit for a set of X and Y data values
         * @param    int     $order   Order of Polynomial for this regression
         * @param    float[] $yValues The set of Y-values for this regression
         * @param    float[] $xValues The set of X-values for this regression
         * @param    boolean $const
         */
        public function __construct($order, $yValues, $xValues = [], $const = true) {
            if (parent::__construct($yValues, $xValues) !== false) {
                if ($order < $this->valueCount) {
                    $this->bestFitType .= '_' . $order;
                    $this->order       = $order;
                    $this->polynomialRegression($order, $yValues, $xValues, $const);
                    if (($this->getGoodnessOfFit() < 0.0) || ($this->getGoodnessOfFit() > 1.0)) {
                        $this->_error = true;
                    }
                } else {
                    $this->_error = true;
                }
            }
        }

        /**
         * Execute the regression and calculate the goodness of fit for a set of X and Y data values
         * @param    int     $order   Order of Polynomial for this regression
         * @param    float[] $yValues The set of Y-values for this regression
         * @param    float[] $xValues The set of X-values for this regression
         * @param    boolean $const
         */
        private function polynomialRegression($order, $yValues, $xValues, $const) {
            // calculate sums
            $x_sum  = array_sum($xValues);
            $y_sum  = array_sum($yValues);
            $xx_sum = $xy_sum = 0;
            for ($i = 0; $i < $this->valueCount; ++$i) {
                $xy_sum += $xValues[$i] * $yValues[$i];
                $xx_sum += $xValues[$i] * $xValues[$i];
                $yy_sum += $yValues[$i] * $yValues[$i];
            }
            /*
             *    This routine uses logic from the PHP port of polyfit version 0.1
             *    written by Michael Bommarito and Paul Meagher
             *
             *    The function fits a polynomial function of order $order through
             *    a series of x-y data points using least squares.
             *
             */
            for ($i = 0; $i < $this->valueCount; ++$i) {
                for ($j = 0; $j <= $order; ++$j) {
                    $A[$i][$j] = pow($xValues[$i], $j);
                }
            }
            for ($i = 0; $i < $this->valueCount; ++$i) {
                $B[$i] = [$yValues[$i]];
            }
            $matrixA = new Matrix($A);
            $matrixB = new Matrix($B);
            $C       = $matrixA->solve($matrixB);
            $coefficients = [];
            for ($i = 0; $i < $C->m; ++$i) {
                $r = $C->get($i, 0);
                if (abs($r) <= pow(10, -9)) {
                    $r = 0;
                }
                $coefficients[] = $r;
            }
            $this->intersect = array_shift($coefficients);
            $this->_slope    = $coefficients;
            $this->calculateGoodnessOfFit($x_sum, $y_sum, $xx_sum, $yy_sum, $xy_sum);
            foreach ($this->xValues as $xKey => $xValue) {
                $this->yBestFitValues[$xKey] = $this->getValueOfYForX($xValue);
            }
        }

        /**
         * Return the Y-Value for a specified value of X
         * @param     float $xValue X-Value
         * @return     float                        Y-Value
         **/
        public function getValueOfYForX($xValue) {
            $retVal = $this->getIntersect();
            $slope  = $this->getSlope();
            foreach ($slope as $key => $value) {
                if ($value != 0.0) {
                    $retVal += $value * pow($xValue, $key + 1);
                }
            }
            return $retVal;
        }

        /**
         * Return the order of this polynomial
         * @return     int
         **/
        public function getOrder() {
            return $this->order;
        }

        /**
         * Return the X-Value for a specified value of Y
         * @param     float $yValue Y-Value
         * @return     float                        X-Value
         **/
        public function getValueOfXForY($yValue) {
            return ($yValue - $this->getIntersect()) / $this->getSlope();
        }

        /**
         * Return the Slope of the line
         * @param     int $dp Number of places of decimal precision to display
         * @return     string
         **/
        public function getSlope($dp = 0) {
            if ($dp != 0) {
                $coefficients = [];
                foreach ($this->_slope as $coefficient) {
                    $coefficients[] = round($coefficient, $dp);
                }
                return $coefficients;
            }
            return $this->_slope;
        }

        /**
         * Return the Equation of the best-fit line
         * @param     int $dp Number of places of decimal precision to display
         * @return     string
         **/
        public function getEquation($dp = 0) {
            $slope     = $this->getSlope($dp);
            $intersect = $this->getIntersect($dp);
            $equation = 'Y = ' . $intersect;
            foreach ($slope as $key => $value) {
                if ($value != 0.0) {
                    $equation .= ' + ' . $value . ' * X';
                    if ($key > 0) {
                        $equation .= '^' . ($key + 1);
                    }
                }
            }
            return $equation;
        }

        public function getCoefficients($dp = 0) {
            return array_merge([$this->getIntersect($dp)], $this->getSlope($dp));
        }
    }
